Respuesta :
Answer:
[tex]rate=-\frac{ d[F_{2}]}{dt}=-\frac{1}{2}*\frac{ d[NO_{2}]}{dt}=\frac{1}{2}*\frac{d[NO_{2}F]}{dt}[/tex]
Explanation:
The rate of a chemical reaction can be measured as how many of moles of a substrate are consumed of moles of products are produced. So it can be expressed as the change in molar concentration of reactant or product over time.
In that sense, we must take in account the stoichiometric coefficients of the reaction. For example, each time a reaction takes place, two molecules of [tex]NO_{2}[/tex] react with one molecule of [tex]F_{2}[/tex] to produce two molecules of [tex]NO_{2}F[/tex].
Also, we use the "-" sign for consumption and leave positive sign for production of a substance.
So, as the question states, one for of expressing the reaction rate is [tex]rate=-\frac{ d[F_{2}]}{dt}[/tex], in other words as the consumption of [tex]F_{2}[/tex] over time.
But it is also possible to express the reaction rate in terms of the other components.
We can say that [tex]rate=-\frac{1}{2}*\frac{ d[NO_{2}]}{dt}[/tex], with negative sign for consumption and the (1/2) to normalize the rate. Note that as the stoichiometric coefficient it's two, the rate of [tex]NO_{2}[/tex] consumption will be twice the reaction rate.
With similar reasoning, we can express the rate of the reaction based on the production of [tex]NO_{2}F[/tex], as [tex]rate=\frac{1}{2}*\frac{d[NO_{2}F]}{dt}[/tex].
The rate of given reaction has been expressed as: [tex]\text {Rate}=-\dfrac{1}{2}\;\dfrac{dNO_2}{dt}=\dfrac{1}{2}\;\dfrac{dNO_2F}{dt}=-\dfrac{dF_2}{dt}[/tex]
The rate of reaction has been given as the amount of reactant disappeared or the amount of product formed in unit time.
The balanced chemical reaction has been:
[tex]\rm 2\;NO_2\;+\;F_2\;\rightarrow\;2\;NO_2F[/tex]
Rate of reaction
The rate of reaction has been expressed in the form of disappearance of any reactant or formation of any product in unit time, with the stoichiometric coefficients.
The rate of the given reaction has been given in the form of disappearance of nitrate, or the formation of nitrate fluoride.
Thus, the form of rate of reaction has been:
[tex]\text {Rate}=-\dfrac{1}{2}\;\dfrac{dNO_2}{dt}[/tex]
The another form for the representation of the rate of reaction for product formation has been:
[tex]\text {Rate}=-\dfrac{1}{2}\;\dfrac{dNO_2F}{dt}[/tex]
Thus, the rate of given reaction has been expressed as: [tex]\text {Rate}=-\dfrac{1}{2}\;\dfrac{dNO_2}{dt}=\dfrac{1}{2}\;\dfrac{dNO_2F}{dt}=-\dfrac{dF_2}{dt}[/tex]
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